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# QSO 510: Module 10 Notes: Wordprocess your answers within this document. Do not create a new file. Show all steps used in arriving at the final...

During the dinner hour, the distribution of the inter-arrival time of customers at a restaurant is estimated to be as shown below. The mode of payment and the service times of the cash and credit card customers are shown in the following tables. Complete the tables and simulate the system for 20 customer arrivals and determine the average time a cash and credit card customer must wait in line before paying the cashier. Use Column A of the given random number table to determine the customer inter-arrival time, Column B to determine whether the customer pays with cash or credit, and Column C to determine the service time.

Inter-arrival time
Inter-arrival Time Probability Cumulative Probability Random Number Interval
30 seconds 0.45
60 seconds 0.25
90 seconds 0.15
120 seconds 0.10
150 seconds 0.05

Mode of Payment
Payment Mode Probability Cumulative Probability Random Number Interval
Cash 0.6
Credit Card 0.4

Cash Service Time
Service Time Probability Cumulative Probability Random Number Interval
20 seconds 0.35
40 seconds 0.30
60 seconds 0.25
80 seconds 0.10

Credit Card Service Time
Service Time Probability Cumulative Probability Random Number Interval
30 seconds 0.20
60 seconds 0.45
90 seconds 0.25
120 seconds 0.10

Random Numbers
(A) (B) (C)
6320 1094 1995
4630 7371 7971
8657 2809 3554
0030 5148 6300
5624 9115 5495
6728 1469 5165
5925 6480 9339
2829 2447 6997
7939 7031 1443
6476 8442 3574
3319 7387 0150
8134 1788 0933
1712 4891 7082
6317 1149 5025
6605 8822 4081
2734 9451 4100
0432 2990 7190
3441 8314 6822
0726 7176 5053
6969 2766 8284

Complete the table below to show the results of the simulation.

Customer Random Number Arrival Time Random Number Mode of Payment Random Number Service Time Service Time Waiting Time
Begins Ends Cash Credit
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20

Average Waiting Time (Cash)=
Average Waiting Time (Credit)=

Please do in word, not excel. Please see attached word file for formatting
Q SO 510: Module 10 Notes: Before doing this assignment, do the practice problem posted under Apply and Discover. Word- process your answers within this document. Do not create a new file. Show all steps used in arriving at the final answers. Incomplete solutions will receive partial credit. Problem During the dinner hour, the distribution of the inter-arrival time of customers at a restaurant is estimated to be as shown below. The mode of payment and the service times of the cash and credit card customers are shown in the following tables. Complete the tables and simulate the system for 20 customer arrivals and determine the average time a cash and credit card customer must wait in line before paying the cashier. Use Column A of the given random number table to determine the customer inter-arrival time, Column B to determine whether the customer pays with cash or credit, and Column C to determine the service time. Inter-arrival time Inter-arrival Time Probability Cumulative Probability Random Number Interval 30 seconds 0.45 60 seconds 0.25 90 seconds 0.15 120 seconds 0.10 150 seconds 0.05 Mode of Payment Payment Mode Probability Cumulative Probability Random Number Interval Cash 0.6 Credit Card 0.4 Cash Service Time Service Time Probability Cumulative Probability Random Number Interval 20 seconds 0.35 40 seconds 0.30 60 seconds 0.25 80 seconds 0.10
Credit Card Service Time Service Time Probability Cumulative Probability Random Number Interval 30 seconds 0.20 60 seconds 0.45 90 seconds 0.25 120 seconds 0.10 Random Numbers (A) (B) (C) 6320 1094 1995 4630 7371 7971 8657 2809 3554 0030 5148 6300 5624 9115 5495 6728 1469 5165 5925 6480 9339 2829 2447 6997 7939 7031 1443 6476 8442 3574 3319 7387 0150 8134 1788 0933 1712 4891 7082 6317 1149 5025 6605 8822 4081 2734 9451 4100 0432 2990 7190 3441 8314 6822 0726 7176 5053 6969 2766 8284
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